Projective Properties of Certain Orthogonal Arrays

Abstract

The projective properties of two-level orthogonal array designs are important in factor screening. General results are given which, in particular, allow the designs derived by Plackett and Burman to be categorized in terms of these properties. The following results are given: 1) every saturated fractional factorial design is of projectivity P=2; 2) a design obtained by doubling is always of projectivity P=2; 3) any saturated two-level design obtained from a orthogonal array constructed by cyclic generation is either a factorial orthogonal array with P=2 or else has projectivity P=3; and 4) any saturated two-level design obtained from an orthogonal array containing n=4m runs, with m odd, is of projectivity P=3.